Prime p₀= 2056537831860574757 starts a Symmetric tuple of 14 consecutive primes, which form 7 twin primes (STPT).
d_n: 0 2 58 2 28 2 10 2 10 2 28 2 58 2 (?)
a_n: 0 2 60 62 90 92 102 104 114 116 144 146 204 206
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 206
Found by: gemini8
db: batch=80, k=14, 2 58 2 28 2 10 2

SPT(16)	2056536740002431847	0 4 70 94 102 154 156 166 240 250 252 304 312 336 402 406	-1091858142910
SPT(16)	2056536964684653469	0 12 30 54 82 88 100 120 232 252 264 270 298 322 340 352	-867175921288
STPT(10)	2056537347793235537	0 2 24 26 42 44 60 62 84 86	-484067339220
SPT(16)	2056537415813326951	0 10 52 66 112 126 186 190 192 196 256 270 316 330 372 382	-416047247806
STPT(10)	2056537528602140957	0 2 90 92 102 104 114 116 204 206	-303258433800
STPT(10)	2056537773587851199	0 2 48 50 60 62 72 74 120 122	-58272723558
TPT(14)	2056537831860574757	0 2 60 62 90 92 102 104 114 116 144 146 204 206	0
SPT(16)	2056537927300381649	0 14 18 24 38 98 102 150 152 200 204 264 278 284 288 302	95439806892
SPT(18)	2056538111417031961	0 28 36 52 108 112 118 130 138 160 168 180 186 190 246 262 270 298	279556457204
STPT(10)	2056538650683439301	0 2 36 38 78 80 120 122 156 158	818822864544
SPT(16)	2056539096114328877	0 2 32 56 62 80 116 132 140 156 192 210 216 240 270 272	1264253754120